One can also solve higher-order equations. For example, in the equation
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| (2.1) |
two solutions are determined by the rational function solver DEtools[ratsols]. Reduction of order then produces a final answer in terms of integrals:
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| (2.2) |
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| (2.3) |
Maple does a quick test to determine if a particular ODE is the symmetric product of a second-order equation. If so, then a solution can be determined from the solutions of the second-order equation. For example, the equation
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| (2.4) |
found in Kamke or Abramowitz and Stegun is the symmetric power of Airy's equation. As such, dsolve produces:
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| (2.5) |
Similarly,
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| (2.6) |
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| (2.7) |
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| (2.8) |
Combined with previous methods, we find that the equation
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| (2.9) |
has a single answer determined from the Maple exponential solver DEtools[expsols], and then reduction of order reduces to a symmetric equation. This gives
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| (2.10) |
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| (2.11) |